That's a red flag for a parent. Coaches can talk all day about pitcher's parents being crazy and entitled but I'd think that of a coach to make demands before my dd was even on the team.
For all of our teams the uniforms, bat bags, and helmets were bought with fees so the player keeps them. We did have one team where the coach bought them back to give to the new player. I've never seen a refund given. The closest thing to it was the coach buying back the equipment.
At a recent camp the coaches said they do check out the social media of players. This is however AFTER they have interest. You need to grab their attention first. The social media is used to check out the personality and character more than anything.